I've been using Therabands for a long time. I like its portability. The past 6 months, I have stopped using them exclusively, switching to dumbbells. Oddly, I experience soreness using db's because I can lift heavier weights. But my objective is to get a lean body like a dancer, not a heavy-duty bodybuilder.
Bands are good when I do Pilates because they up the intensity of the exercise.
Is your fitness trainer female? I notice females tend to go for bands. I was introduced to bands when I worked part time at a physical therapists' center back in college.